INFLUENCE OF SURFACE ROUGHNESS AND WAVINESS A surface deformation analysis considers the influence of

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  • INFLUENCE OF SURFACE ROUGHNESS

    AND WAVINESS UPON THERMAL CONTACT

    RESISTANCE

    Milan M. Yovanovich

    Warren M. Rohsenow

    Report No. 76361-48

    Contract No. NAS7-100

    Department of Mechanical

    Engineering

    Engineering Projects Laboratory Massachusetts Institute of

    Technology

    _une 1967

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    https://ntrs.nasa.gov/search.jsp?R=19680003701 2020-03-19T21:01:51+00:00Z

  • RE-ORDER NO. _:_ 7"_/'_

    Technical Report No. 6361-_8

    INFLUENCE OF SURFACE ROUGHNESS AND WAVINESS

    UPON THERMAL CONTACT RESISTANCE

    by

    M. Michael Yovanovich

    Warren M. Rohsenow

    Sponsored by the National Aeronautics

    and Space Administration

    951621

    Contract No. Nas T-lOO

    June 1967

    Department of Mechanical Engineering

    Massachusetts Institute of Technology

    Cambridge, Massachusetts 0P-139

  • -2-

    ABSTRACT

    This work deals with the phenomenonof thermal resistance between

    contacting solids. Attention is directed towards contiguous solids

    possessing both surface roughness and wBviness. ]_en two such surfaces

    are brought together under load, they actually touch at isolated micro-

    contacts, and the resulting real area is the sumof these microcontacts.

    Because of the waviness the microcontacts are confined to a region

    called the contour area which mayoccupy some fraction of the total

    available area. The non-uniformpressure distribution over the con-

    tour area results in microcontacts which vary in size and density. In

    the absence of an interstitial fluid and negligible radiation heat trans-

    fer, all the heat crossing the interface must flow through the microcon-

    tacts. A thermal analysis, based on size and spatial distribution,

    results in a thermal resistance equation which differs from previously

    developed theories. The equation is verified by liquid analog tests

    which show that the size and spatial distribution_revery significant.

    A surface deformation analysis considers the influence of surface

    roughness upon the elastic deformation of a rough hemisphere. An equa-

    tion is developed which shows the extent of the contour area as a func-

    tion of the surface geometry, the material properties, and the applied

    load. The equation is comparedwith existing theories and qualitatively

    checked against experimental results.

    Experimental heat transfer data were obtained to verify the thermal

    and deformation theories. The agreementbetween theory and test is

    quite good over a large range of surface geometry and applied loads.

  • -S-

    ACKNOWLED(_ENTS

    The author wishes to acknowledge the assistance and _Ivice of

    his Thesis Committee which consists of Professors Warren M. Rohsenow,

    Henri Fenech, Brandon G. Rightmlre, and Michael Cooper. He particularly

    wishes to acknowledge the encouragement of his thesis supervisor, Pro-

    fessor Warren M. Rohsenow, and the many long and fruitful discussions

    with Professor Michael Cooper.

    The author also extends his heartfelt thanks to his colleagues in

    thermal contact resistance research: Professor Bora Mikic of the Depart-

    ment of Mechanical Engineering, Dr. Thomas J. Lardner of the Department

    of Mathematics, and Slmjros Flengas. Professor Mikic and Mr. Fleng_s

    shared with me the results of their liquid analog tests. Dr. Lardner

    acted as a sounding board for some of my ideas on contact resistance and

    the deformation of solids.

    The author would be remlse if he did not acknowledge the mlvice

    and aid of Mr. Frederick Johnson of the Heat Transfer Laboratory, whose

    experience enabled the author to accomplish quickly and efficiently some

    of the fabrication work.

    Finally the author expresses his thanks to his wife for her patience

    and encouragement.

    Sincere appreciation is expressed for the financial support of the

    National Aeronautics and Space Administration under NASA Contract NAS 7-100

    which made this work possible.

  • -4-

    TABLE OF CONTENTS

    Page

    ABSTRACT ............................ 2

    ACKNOWLE_ ........................ 3

    _LEOF_NTENTS ....................... 4

    LIST OF FIGURES ....................... 7

    NOMENCLAZJaE ......................... 9

    I. INTRODUCTION ........................ 12

    1.1 Historical Background

    1.2 Review of Parameters Affecting Thermal Contact Resistance

    1.2.1 Effect of Apparent Contact Pressure

    1.2.2 Effect of Metal Thermal Conductivities

    1.2.3 Effect of Surface Roughness 1.2.4 Effect of Surface Waviness

    12

    14

    15

    17

    17 18

    1.2.5 Effect of Interstitial Fluid Thermal Conductivity 19

    1.2.6 Effect of Material Hardness 19

    1.2.7 Effect of Modulus of Elasticity 1.2.8 Effect of Mean Contact Temperature Level 1.2.9 Effect of Interstitial Fluid Pressure

    1.2.10 Effect of Relaxation Time

    1.2.11 Effect of Filler Material 1.2.12 Directional Effect

    1.3 Summary of Parameters Influencing Thermal Contact Resistance

    19 2O

    21

    22

    22

    23

    2. _ CON_ACT RESISTANCE ................. 27

    2.1 Introduction

    2.2 General Theory of Thermal Contact Resistance

    2.3 Thermal Contact Resistance for an Elemental Heat Channel

    3. THE EFFECTS OF CONTACT SPOT SIZE AND MALDISTRIBUTION ....

    27 30

    34

    41

    3.1 Contact Between Nominally Flat, Rough Surfaces 3.2 Elemental Heat Flux Tube

    3.3 Effect of Variable Contact Spot Size

    3.4 Effect of Maldistribution of Contact Spots

    3.5 Contact Resistance Between Rough, Wavy Surfaces

    41

    42 _6

    29

    51

  • -5-

    4. SURFACE DEFOI_4ATION ....................

    4.I Introduction

    4.2 Elastic Deformation of a Smooth Hemispherical Surface

    4.3 Contact Between Nominally Flat, Rough Surfaces 4.4 Depth of Distributed Stress Region

    4.5 Local Displacements Due to Plastic Deformation of

    Asperities 4.6 Elastic Deformation of a Rough Hemispherical Surface

    5. DESCRIPTION OF THE APPARA._JS ...............

    5.1 Introduction

    5.2 Surface Preparation Device

    5.3 Surface Measurement Device 5.4 Experimental Apparatus for Obtaining Contact

    Resistance Data

    5.5 Surface Deformation Apparatus 5.6 Liquid Analog Apparatus

    6. EXPFffUMENTALPROCEDUREANDTEST_TS

    6.1 Liquid Analog Tests

    6. i.1 Maldistribution Tests

    6.1.2 Effect of Variable Contact Spot Size

    6.2 Thermal Contact Resistance Tests

    6.2.1 Preparation of Test Specimens 6.2.2 Vacuum Tests

    6.3 Surface Deformation Tests

    7. SURFACE PROFILE ANALYSIS .................

    7.1 Introduction

    7.2 Surface Profile Theory

    7.3 Number, Size, and Real Area of Contact Spots

    8. COMPARISON OF PREDICTED AND EXPERIMENTAL RESULTS .....

    8.1 Introduction

    8.2 Theoretical Heat Transfer Models

    8.3 Comparison of Models with Heat Transfer Data 8.4 Surface Deformation Models

    9. CONCLUSIONS ........................

    9-i Discussion of Results

    9-2 Recommendations for Future Research

    Page

    56

    56 58 62 69

    7O

    73

    8O

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    8o 81

    82

    84 84

    86

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    92

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    92 93

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    96 96

    i00

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  • -6-

    Page

    BIBLIOGRAPHY .......................... 107

    APP_DIX A - CONTACT SPOTS ARE ALL ISO_ ......... llO

    APP_DIX B - ASYMMETRIC HEAT FLUX TUBE ............. ll8

    APPENDIX C - AVERAGE CONTACT SIZE INDEPENDENT OF LOAD ..... 123

    APPENDIX D - HEAT TRANSFER DATA ................ 128

    BIOGRAPHICAL NOTE ....................... 138

  • -7-

    LIST OF FIGURES

    Fig. 1

    Fig. 2

    Fig. 3

    Fig. 4

    Fig- 5

    Fig. 6

    Fig. 7

    Fig. 8

    Fig. 9

    Fig. i0

    Fig. ii

    Fig. 12

    Fig. 13

    Fig. 14

    Fig. 15

    Fig. 16

    Fig. 17

    Fig. 18

    Fig. 19

    Fig. 20

    Fig. 21

    Fig. 22

    Fig. 23

    Fig. 24

    Temperature Distribution in Contacting Solids

    Effect of Various Parameters on Thermal Contact Resistance

    Typical Linear Profile of Blanchard Ground Surface

    Typical Linear Profile of Bead Blasted Surface

    Typical Linear Profile of Bead Blasted Surface

    Typical Linear Profile of Wavy, Rough Surface

    Distribution of Asperity Heights

    Enlargement of Exposed X-Ray Film

    Elemental Heat Flux Tube with One Contact Spot

    Elemental Heat Flux